The difference with Tryndamere and other melee carries is that he has an ultimate that makes him immune to death (except spawn turret), therefore he can do some damage pop his ultimate, maybe die but has done loads of damage already helping the team immensely.

Melee AD carries are generally great at backdooring. Anyways who plays Yi AD, his AP is far superior.

Jungling with Trynd is risky. First you need runes for him, he's one of the more rune/mastery dependent junglers in the game. He's one of the hardest carries from the jungle, but he either falls on his face or shoves other people faces down. Usually your first buy would be a PD, you get enough innate AD and Crit from Q.

Funny, I found jungling as Tryndamere on a level one alt just fine.

But I guess you're someone who truly believes Runes and Masteries make much of a difference.